Steven Payne, 37, was attacked about noon on Monday at Wharton Beach, east of Esperance in Western Australia.
A large sea and coastal search has failed to find his remains and WA police on Wednesday said it had been suspended "pending any new information being received".
Drone footage shot by a witness of the attack showed a shark swimming away from a large cloud of blood close to the shore and a surfboard with bite marks was recovered from the water.
Police previously said the search was a recovery operation, not a rescue.
Mr Payne, his partner and his "loving dog" were on a six-month travelling holiday when the "heartbreaking" incident happened.
The presumed death is the fourth fatal shark attack since 2017 in the area, about 800km south of Perth.
